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The Brachistochrone

Support Vsauce, your brain, Alzheimer's research, and other YouTube educators by joining THE CURIOSITY BOX: a seasonal delivery of viral science toys made by Vsauce! A portion of all proceeds goes to Alzheimer's research and our Inquisitive Fellowship, a program that gives money and resources directly to growing science channels here on YouTube! https://www.curiositybox.com BRAIN CANDY LIVE: http://www.braincandylive.com Links to sources and to learn more below! MY TWITTER:   / tweetsauce   MY INSTAGRAM:   / electricpants   THE CURIOSITY BOX: https://www.curiositybox.com/ Stan Wagon “Roads and Wheels” [PDF]: http://web.mst.edu/~lmhall/Personal/R... 3Blue1Brown video, “The Brachistochrone, with Steven Strogatz”:    • The Brachistochrone, with Steven Stro...   Pile of people visualization originally from this Vsauce1 video:    • How Many Things Are There?   Online spirograph: http://nathanfriend.io/inspirograph/ The Brachistochrone http://whistleralley.com/brachistochr... Rolling: http://www.animations.physics.unsw.ed... http://teacher.pas.rochester.edu/phy1... Refraction of light: http://www.physicsclassroom.com/class... http://www.funscience.in/study-zone/P... http://www.walter-fendt.de/html5/phen... http://micro.magnet.fsu.edu/primer/ja... http://astro.unl.edu/classaction/anim... http://demonstrations.wolfram.com/Fer... Feynman on The Principle of Least Time: http://www.feynmanlectures.caltech.ed... cycloid as answer to brachistochrone: https://sinews.siam.org/About-the-Aut... Music from:    / jakechudnow   and http://www.audionetwork.com Roulette animations by Eric Langlay    / ericlanglay   good relevant Wikipedia articles: https://en.wikipedia.org/wiki/Brachis... https://en.wikipedia.org/wiki/Tautoch... https://goo.gl/SlRDhK https://en.wikipedia.org/wiki/Cycloid https://en.wikipedia.org/wiki/Snell's... Wolfram demonstration projects used: "Cycloid Curves" from the Wolfram Demonstrations Project  http://demonstrations.wolfram.com/Cyc... Contributed by: Sean Madsen Additional contributions by: David von Seggern (U. Nevada, Reno) "Shaping a Road and Finding the Corresponding Wheel" from the Wolfram Demonstrations Project  http://demonstrations.wolfram.com/Sha... Contributed by: Stan Wagon (Macalester College)